{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction to Quantitative Finance\n",
    "\n",
    "Copyright (c) 2019 Python Charmers Pty Ltd, Australia, <https://pythoncharmers.com>. All rights reserved.\n",
    "\n",
    "<img src=\"img/python_charmers_logo.png\" width=\"300\" alt=\"Python Charmers Logo\">\n",
    "\n",
    "Published under the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) license. See `LICENSE.md` for details.\n",
    "\n",
    "Sponsored by Tibra Global Services, <https://tibra.com>\n",
    "\n",
    "<img src=\"img/tibra_logo.png\" width=\"300\" alt=\"Tibra Logo\">\n",
    "\n",
    "\n",
    "## Module 2.4: Residual Analysis\n",
    "\n",
    "### 2.4.1 - Residual Analysis\n",
    "\n",
    "The residuals, or errors, are the difference between your predicted model and the actual values observed. Residuals are almost always there - natural variance causes random fluctuations, and our model may not incorporate all relevant information to analyse.\n",
    "\n",
    "Residuals can help you identify what changes to make to your model, and allow you to check your assumptions about the model are correct.\n",
    "\n",
    "In this module, we will revisit some of the concepts we have looked at in previous modules, but specifically with a focus on the residuals of a model. Previous notebooks generally looked at the data itself before the model is fit, rather than after.\n",
    "\n",
    "#### Exercise\n",
    "\n",
    "Research \"Anscombe's Quartet\". What does it tell you about linear regression? How can residual analysis assist in finding issues caused by this type of problem?\n",
    "\n",
    "Note: In this notebook we will only use simple linear regression models, but the analysis techniques are applicable to any model.\n",
    "\n",
    "Let's start with a model that is accurate with regards to the data it is modelling:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%run setup.ipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(-10, 10, 100)\n",
    "# y = 3x + 5 + e\n",
    "y_linear = x * 3 + 5 + np.random.random(len(x)) * 15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x236a577d390>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y_linear, 'bo', alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now fit a linear model, and then review the residuals of this model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm\n",
    "X = sm.add_constant(x)\n",
    "model = sm.OLS(y_linear, X)\n",
    "results = model.fit()\n",
    "y_pred = results.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x236a967aed0>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y_linear, 'bo', alpha=0.5)\n",
    "plt.plot(x, y_pred, 'r-', alpha=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate the residuals\n",
    "e_linear = y_pred - y_linear"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.LineCollection at 0x236a4fd11d0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Residual analysis - Linear\")\n",
    "plt.plot(x, e_linear, 'ro')\n",
    "plt.hlines(0, xmin=x.min(), xmax=x.max())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this plot, our linear model fits our linear data very well. As seen in the above plots, there is variability, but this residual plot, which plots the residuals against the x values, you can see a few very important components:\n",
    "\n",
    "1. The errors are centred around 0\n",
    "1. The errors look random, i.e. there are no trends\n",
    "1. The variability of the errors does not change\n",
    "\n",
    "We will now look at some examples of each of these three components not being seen.\n",
    "\n",
    "### Errors Centred Around 0\n",
    "It is a property of the linear regression model that errors will be centred around 0. In other words, regardless of your data, your residuals will be centred around zero. More formally, the expected value of the errors will be 0. For instance, here is a sine curve with a linear model fitted, and you can still see the errors are centred around zero:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x236a9896290>]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_sin = np.sin(x)\n",
    "plt.plot(x, y_sin)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x236a9920d50>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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7BJPOypX+ys8JA9NykGIjeF0PP7QA8I5pfyMIHSel0p4m7A4aNEi9evVSa2trp9tbW1tVWlqa0WMcfvjhGjNmjDZt2pTw54WFhSosLMx6X5EBqlv8y28J3amkG8GLROwRvJoaTq5uqa+3X/NDR7CHD7enHQkSYSBPp4169+6t0047TStWrIjf1tHRoRUrVnQaiUklGo3q3Xff1VAqJvKP6ha4gf40uUWeGgLI82qjmTNn6te//rUeeeQRrV+/XldffbX27t2rqVOnSpIuueQSzZ49O779/Pnz9V//9V/63//9X7311lv6x3/8R3344Ye64oorvN5VpEN1C9zACF7uhCVPjcTv0PG8z8tFF12kjz/+WHPmzFFLS4tOPfVUvfDCC/Ek3i1btqig4MsY6v/+7/80bdo0tbS06KijjtJpp52mVatW6Wtf+5rXu4p0YtUtEyfagUqi5Qr8Xt2C/GMEL3ecjHKZMu3YFVNiocTaRnAu0cGivNwOXDhYIJ3YmkzNzYlHBFiTyT1Ll9qVXOnU1dkt4E1D4negsLYRvMVyBchGEPrTmCLIo1xhmRJDQgQv6BkfL9gFA5jcn8YkQc5TI/E71DzPeUEP0I8BYVBba5dD87funSDnqZH4HWoEL35D8hnCxKT+NKaKjXIlOq6YnKcW5CkxpEXCrp+QfAbAK0Eb0SXxO3CcnL8JXvwi9kFMNofLBxEAOot94ZMST4nxhc8oVBuZiOQzAHCGxO/QIufFL0g+AwDnSPx2j0FTiwQvfkHyGQD0DInf2TOsWIRpI78Icj8GAIB/Gbh4J8GLX9B1FACQa4Z2KiZ48ROSzwAAuWRosQg5L35D8hkyYVBiHQAfM7RYhODFj0g+QyqGJdYB8DFDi0WYNgJMYmBiHQAfM7RYhOAF7olGpYYGaelS+9pnCV7GMzSxDoCPGVosQvACd9TX28sbjBsnTZ5sX1dUMBLgJkMT6wD4nIHFIuS8IHvJFpSMTWX49I/fOIYm1gEwgGHFIgQvyE66qYxIxJ7KqKnx7YfAGIYm1gEwhEHFIkwbITtMZeSOoYl1AOA2ghdkh6mM3DE0sc4xEr8BpEHwguwwlZFbBibWOULiN4AMRCwrUbKCudrb21VcXKy2tjYVFRXle3eCLxq1Ty7NzYnzXiIR+8Ta1GT+iICfBLHDbrLE79ioUhCCMwBJOTl/E7wge7GTjtT5xMNJB5mKBcHJ8qcIgoHAc3L+ZtoI2Qv6VAa8R+I3AAcolYY7DOsRAJ8h8dtdQZxWBA5B8AL3GNQjAD5D4rd7WLiT4C0EmDYCkH/0sHEHC3dSsRYSBC8A8i8sPWy8xMKdBG8hQvDiBzTlAkj8zlbYk54J3kKFnJd8Y34a+BKJ3z0X9qRnJ8EbuXnGI3jJJ1ZjBroj8btnwp70HPbgLWSYNsoXhjgBuCnsSc9hD95ChuAlX8I+Pw3AXWFPeg578BYyBC/5whAnALeFOek57MFbyBC85AtDnAC8UFsrbd4srVwp1dXZ101NwQ5cYsIcvIUMCzPmC6sxA4A36LBrJCfnb6qN8iU2xDlxoh2oJFqNmSFOAHCOirXAY9oonxjiBADAMUZe8o2mXACAXDN8ao3gxQ8Y4gQA5EoAOrszbQQAQFgEZPFKghfA71i4E4AbAtTZneAF3uGkm736erukftw4afJk+7qiwphvRwB8JECd3Qle4A1OutkLyPAuAJ8IUGd3ghe4j5Nu9gI0vAvAJwLU2Z3gBe7ipOuOAA3vAvCJAC1eSfACd3HSdUeAhncB+ESAFq8keIG7OOm6I0DDuwB8JCCd3WlSB3dx0nVHbHg33cKdBgzvZs3wTqCA7wSgszvBC9zFSdcdLNxpC0AnUMCXDO/szrQR3BWgOdW8C8jwbo9RtQYgiYhlJfp6bK729nYVFxerra1NRUVF+d6d8Er0jbm83A5cgn7SdVsYp02iUbsvULLk79gIXlNT8F8LICScnL8JXuCdMJ504Y6GBruxYTorVxo99A3gS07O3+S8wDuGz6kij6haA5ACOS8A/IeqNQApMPICwH+oWnOGKdr0eI0ChZEXAP5D1VrmWAQ1PV6jwCF4AeBPYS8VzwTl5OnxGgUS1Ua5xtAl4AyfmcQoJ0+P18goVBv5Fd1CAeeoWkvMySKoYX39eI0Ci2mjXGHoEoCbKCdPj9cosAheciEatUdcEs3QxW6bMcPeDgAyQTl5erxGgUXwkgtOhi4BIBOxcvKu1VgxkYi9JEeYy8l5jQKL4CUXGLoE4DbKydPjNQqsnAQv9913nyoqKtSnTx9VVlbq9ddfT7n9U089peOPP159+vTRSSedpOeffz4Xu+kdhi4BeIFy8vR4jQLJ81LpJ598UpdccokWL16syspKLVq0SE899ZQ2btyoIUOGdNt+1apVOvPMM7VgwQJ973vfU11dnX7+85/rrbfe0oknnpj29/myVDpWrpeuWyjlegB6gnLy9HiNfM9Xq0pXVlbqm9/8pu69915JUkdHh8rLy3Xttdfqpptu6rb9RRddpL179+r3v/99/La/+Zu/0amnnqrFixen/X2+DF6kL6uNpM4BTGzokm8AAIAQc3L+9nTaaP/+/VqzZo2qq6u//IUFBaqurlZjY2PC+zQ2NnbaXpImTJiQdPt9+/apvb2908WXGLoEAMAVnjap++STTxSNRlVSUtLp9pKSEm3YsCHhfVpaWhJu39LSknD7BQsWaN68ee7ssNdqa6WaGoYuAQDIgvEddmfPnq2ZM2fG/9/e3q7y8vI87lEadAsFAORawHJ+PA1eBg0apF69eqm1tbXT7a2trSotLU14n9LSUkfbFxYWqrCw0J0dBgAgaAK4NI2nOS+9e/fWaaedphUrVsRv6+jo0IoVK1RVVZXwPlVVVZ22l6Tly5cn3R4AACQR0KVpPJ82mjlzpi699FKdfvrpOuOMM7Ro0SLt3btXU6dOlSRdcsklGjZsmBYsWCBJuu6663TWWWfpzjvv1HnnnacnnnhCb775pn71q195vavIhYANXXqC1wiAG9ItTROJ2EvT1NQYd4zxPHi56KKL9PHHH2vOnDlqaWnRqaeeqhdeeCGelLtlyxYVFHw5ADR27FjV1dXp5ptv1k9+8hMdd9xxeuaZZzLq8QKfC+DQpet4jQC4JcCranve5yXXfNvnJexiQ5dd/9zoc/MlXiMAblq6VJo8Of12dXXSpEne708avunzAkhiVe1M8BoBcFuAl6YheIH3WFU7PV4jAG4L8KraBC/wHqtqp8drBMBtAV5Vm+AF3gvw0KVreI0AeCGgS9OQsAvvsap2erxGzlBODjhjwGeGhF34S4CHLl3Da5S5+no70Bs3zq6kGDfO/r+hzbaAnIgtTTNpkn1t+LGE4AW5EdChS1fxGqUX0G6hAJxh2gi5ZcDQZd7xGiUWm1pLVpXF1BpgNCfnb+NXlYZhWFU7PV6jxALcLRSAM0wbATAD5eQA/oqRFwBmoJwcbmJ61mgELwDMEOsWmq6c3MBuoY5w0s0eC6Aaj2kjAGagnJwycTdQsRYIBC8AzBHmcnJOutljAdTAoFTaawzxAu4L2+eKMnF3NDTYo1XprFxJxVoeUCrtF8yrAt4IWzk5ZeLuoGItMJg28gpDvADcwknXHVSsBQbBixeYVwXgJk667ohVrHVN+I6JRKTy8uBXrAUAwYsXnAzxAkA6nHTdQcVaYBC8eIEhXgBu4qTrnjBXrAUIwYsXGOIF4DZOuu6prZU2b7ariurq7OumJl5Dg1Aq7YVYWWO6TqCUNQJwKmxl4ggNSqXzLTbEO3GiHagcGsAwxAsgG2ErEwcSYNrIKwzxAgDgCUZevFRbK9XUMMQLAMidEEwtErx4jSFeAECuhKSzO9NGAAAEQYg6uxO8IL+iUXuxtKVL7Wu6DgOAcyHr7E7wgvypr7dLyseNkyZPtq8rKgL17SAtgjcAbghZZ3eCF+RHiIY3kyJ4A+CWkHV2J3hB7oVseDMhgjcAbgpZZ3eCF+ReyIY3uyF4A+C2kC3eSfCC3AvZ8GY3YQ/eALgvZIt3Erwg90I2vNlN2IM3L5D4DISqsztN6pB7seHNdAtXBmR4s5uwB29uC0lTLiAjIenszqrSyI9YwqqUeOHKgH1L6IRVx90T+zvq+jqG4e8ICBgn52+mjZAfIRre7CZkc9OeIfEZCC2CF+RPba20ebO0cqVUV2dfNzUFO3CJCXPw5hYSn4HQIucF+RXmhStDMjftGRKf4bYQrMYcFAQvQD6FOXjLFonPcBOJ30Zh2giAmULWlAseouO1cQheAJgpLInP9LDxFonfRiJ4AWCuoCc+s3in90j8NhI5LwDMFtTE52Q9bGJTGUEIzvyAxG8jEbwAMF/QEp/TTWVEIvZURk2N+UFavpH4bSSmjQDAb5jKyB0Sv41E8OImEusAuIGpjNwJS+J3wBC8uIXEOgBuYSojt4Ke+B1ALMzoBhaHA+AmFu/MDzrs5pWT8zfBS7ZiB5lk89McZAD0RJhXXkcosap0LpFYB8ALTGUASVEqnS0S6wB4Jag9bOCekE51Ebxki8Q6AF4KWg8buCfEi0kybZQtegQAAHIt5ItJErxkix4BAIBcYjFJghdXkFgHAMgVCkXIeXENiXXuCWkCGgBkhEIRghdXkViXvRAnoAFARigUYdoIPhLyBDQAyAiFIgQv8ImwJKCxeCeAbFEoQvACnwhDAhqLdwJwS8gLRch5gT8EPQEt2eKdsSmxEBxsco7EbwRdiAtFCF7gD0FOQEs3JRaJ2FNiNTWhOOjkBInfCIuQFoowbQR/CHICWhimxPyExG+4hRw13yJ4gT8EOQEt6FNifhKWxG94jxw1XyN4gX8ENQEtyFNifsMoF9zA6J3veRq87Ny5U1OmTFFRUZH69++vyy+/XHv27El5n7PPPluRSKTT5aqrrvJyN+EntbXS5s3SypVSXZ193dRkbuAiBXtKzG8Y5UK2GL0zgqcJu1OmTNGOHTu0fPlyHThwQFOnTtWVV16purq6lPebNm2a5s+fH/9/3759vdxN+E3QEtBiU2ITJ9qByqEHRdOnxPyGUS5ky8noXZCOU4bxbORl/fr1euGFF/TAAw+osrJS3/rWt3TPPffoiSee0Pbt21Pet2/fviotLY1fioqKvNpNIDeCOiXmN4xyIVuM3hnBs+ClsbFR/fv31+mnnx6/rbq6WgUFBVq9enXK+z7++OMaNGiQTjzxRM2ePVufffZZ0m337dun9vb2ThfAl4I4JeY3pid+U92Sf4zeGcGzaaOWlhYNGTKk8y877DANGDBALS0tSe83efJkjRgxQmVlZXrnnXd04403auPGjapPkiC1YMECzZs3z9V9BzwTtCkxP4qNciXq87JokX+DRXrT+ENs9K65OXHeSyRi/5zRu7xyPPJy0003dUuo7XrZsGFDj3foyiuv1IQJE3TSSSdpypQpevTRR/X000/rgw8+SLj97Nmz1dbWFr9s3bq1x78bQECYNspFdYt/mD56FxKOR15mzZqlyy67LOU2xxxzjEpLS/XRRx91uv3gwYPauXOnSktLM/59lZWVkqRNmzZp1KhR3X5eWFiowsLCjB8PQEiYMspFB2b/MXX0LkQcBy+DBw/W4MGD025XVVWlXbt2ac2aNTrttNMkSS+//LI6OjriAUkm1q5dK0kayvwigCCiusWfQrxukAk8y3k54YQTdM4552jatGlavHixDhw4oGuuuUYXX3yxysrKJEnNzc0aP368Hn30UZ1xxhn64IMPVFdXp+9+97saOHCg3nnnHV1//fU688wzdfLJJ3u1qwCQP1S3+JcfR+9YcFSSx31eHn/8cV1zzTUaP368CgoKdMEFF+juu++O//zAgQPauHFjvJqod+/eeumll7Ro0SLt3btX5eXluuCCC3TzzTd7uZsAkD9UtyBTJHXHRSwr0USrudrb21VcXKy2tjZv+8MQ/QJwQzRqr5mTrrqlqYljTJjFkrq7/o3EkogD0C/KyfmbtY16ggW7ALiF6hakw5IF3RC8OEVJIwC30YEZqbDgaDee5rwEDiWNALxCdQuSIam7G4IXJyhpBOAlP1a3IP9I6u6GaSMniH4BALnGgqPdELw4QfQLAMg1krq7IXhxgugXAJAPJHV3Qs6LE7Hod+JEO1A5NHE3pNFvztBXB4Af5PNYRFJ3HMGLUyzYlXt0lYQbCICRLT8ci0jqlkSH3Z7jQJgbJneV5G/EP/xw0oHZTD4WGcLJ+ZvgBf4Va5uerDzdz23TOVn6BycdZMvkY5FBWB4AwWBqV0m6MPsHbdXhBlOPRQFG8AL/MrGvDidLf+GkAzeYeCwKOIIX+JeJfXU4WfoLJx24wcRjUcARvMC/TOyrw8nSXzjpwA0mHosCjuAF/mViV0lOlv7i95NONCo1NEhLl9rXTCf6k4nHooAjeIG/mdZV0u8ny7Dx80mnvt6uYBk3Tpo82b6uqCCh26/ycSwiuE2KUmmYwaSeKbFqIylxF2Y/Bl1Bl6h0vbw8f40lKd82V66ORSFst0CfF4IX5JvfTpbwTwBMzxCkE9LgluCF4AV+4JeTJfylocGeIkpn5UrawIdRiINbJ+dv1jYCvMIaJEiEijSk4qTdQoiPLyTsAkAuUZGGVAhuM0LwAgC5REUaUiG4zQjBCwDkkp/Lt9EzbpY0E9xmhOAFAHLNtP5FSM7tfj0Etxmh2ggA8oWKNLN5WdIcwnYLlEoTvAAAvJSLkuaQBbeUSnshZH9EAIAUclHSTLuFpAheMhHCNs0AgBQoac4rEnbTic1pdo2wm5vt21lEDTAXC9+hpyhpzityXlIJcZtmIPAYUUU2YueH5ubuCbtSz84PIU9PcHL+ZuQlFSdzmsgtvjEjG4yoIltulzS7XXIdcAQvqTCn6U98yJGNaNQecUn0bTl224wZBMRIz61+PQTTjhG8pMKcpv/wIUe2GFGFm2prpc2b7VXA6+rs66amzAMXgukeodoolVib5nRzmiFv05wz6T7kkYj9Ia+pyc88ccjnq43BiCrc1rWkOTatncmxgFWke4SRl1Ro0+wvfv7GzFSWOfI1okqeVjg4PRYQTPcIwUs6rEHiH379kDOVZZZ8LHxHcBsOPTkWkJ7QIwQvmch2ThPu8OOHnPlq8+R6RJXgNhycHgtiI3HNzdLgwawi7RB9XmAOL/oqZKuhwf4Wnc7KlcxX+00uFr6jV1R4ODkW7NzZ/W8vETcWeDQIfV4QTH7MQfLrVBbSy8WIqp/ztOCuTD/jt98uXXBB+sBFIj0hBaqNYJZYDlKizqj5WCrej1NZyJzXC98R3IZHpp/xP/wh9c8HD5YWLrTzLKlYTIrgBeaprbXLof1Qlkw5PVIhuA2PdMeCTH38sR24MM2cEtNGMFPsG/OkSfZ1vr6d+HEqC/6Rj8om5EeqY4FTjMSlRfACZItyeiRDcBsuyY4FTjESlxbVRoBb6LCLZHJR2QT/iB0Lfvtb6d57M79fyKvPnJy/CV4AIMbLAJTgNnwyLZ+WQlcWnYiT8zcJuwAgJR4dGT7cnvZx42TidWUT/MdJEm++KiYNRc4LANAFF17IJIl3xgy6tvcAwQuAcGOJB3gpWRJvebmdE7NwYX4rJg3FtBGAcHPSBdfJtA85LojxU2+qgCB4ARBuXnTB9Tp/BuYh58lVTBshOGKrtC5dal8zzI9MuN0Fl/wZwHMELwiG+np79d5x46TJk+3rigpOFEjPzS645M8AOUHwAvPl45suozzB4WYXXFaRBnKC4AVmy8c3XUZ5gsetJR5YRRrICRJ2YTavKkWSiY3ydA2WYqM8Ie6OabxkFSGSPbqWSZUIq0gDOUHwArPl8ptuulGeSMQe5ampoQTSVF0rQpxWDaXrqBpbu4ZVpIGsMG0Es+Xymy75DOHiJJcqlgO1bJk0bZp9G6tIA55h5AVmy+U3XfIZwsPJKNuzz3YfnRk40L7+9NMvb2PtGsA1BC8wW6xSZOJE+4Ry6MnG7W+65DOER6ajbBdfbOc5dbVzp73NvHnSccfRURVwGdNGMJ9blSLpuNkPBP6W6ehZosBF+nJ05oEHpB/8gLVrAJcRvCAYamulzZvt1Vnr6rxZpdXNfiDwNzdGz8iBAjxD8ILgiFWKTJrk3TfdXI3yIL/SjbI5QQ4U4DpyXgCnWCE2+FLlUjlFDhTguohlZfOp9J/29nYVFxerra1NRUVF+d4dACZL1OclU7FKt6YmAlsgA07O355NG/3sZz/T2LFj1bdvX/Xv3z+j+1iWpTlz5mjo0KE64ogjVF1drffff9+rXQSA1A7Npbr55szvRw4U4CnPgpf9+/frwgsv1NVXX53xfW6//XbdfffdWrx4sVavXq2vfOUrmjBhgr744guvdhNBxuKJcEMsl+qWWzLPgyEHCvCU59NGS5Ys0YwZM7Rr166U21mWpbKyMs2aNUv/+q//Kklqa2tTSUmJlixZoosvvjij38e0ESQ5b+sOZCLWdVdKnAcTa1xHDhTgmC+mjZxqampSS0uLqqur47cVFxersrJSjY2NSe+3b98+tbe3d7og5Jy0dc8EIziISVZtVl4u/fa30sKF9HQBcsA3wUtLS4skqaSkpNPtJSUl8Z8lsmDBAhUXF8cv5eXlnu4nfC5dW3fJ/nacaQBSXy9VVEjjxkmTJ9vXFRXOAyAERy56CgFIyVHwctNNNykSiaS8bNiwwat9TWj27Nlqa2uLX7Zu3ZrT3w+fcXPxRLdHcBAcuegpBCApR31eZs2apcsuuyzlNsccc0yPdqS0tFSS1NraqqGH9EVobW3VqaeemvR+hYWFKiws7NHvRAC5tXiik4X5OHEBQE45Cl4GDx6swYMHe7IjI0eOVGlpqVasWBEPVtrb27V69WpHFUsIObcWT3QygnP22RnvHgAge57lvGzZskVr167Vli1bFI1GtXbtWq1du1Z79uyJb3P88cfr6aefliRFIhHNmDFDt956q373u9/p3Xff1SWXXKKysjKdf/75Xu0mgsatxRPdGsEBALjOs+UB5syZo0ceeST+/zFjxkiSVq5cqbP/+k1148aNamtri29zww03aO/evbryyiu1a9cufetb39ILL7ygPn36eLWbCJpUbd2dNA5zawQHAOA6lgdAMCXq81JebgcumVSFRKN2VVFzc+K8F1q/A4CrnJy/WZgRwZRs8UTJ7tWSbkFFt0ZwAACuI3hBcMXKWWMy7bobjdpBz759dkv4X/+6+30yHcEBALiO4AXhEOvZ0nUKKNazJbYOTaIAZ9gwad486bjjUo/WAABygpwXBF8sfyVV6fOAAdK110rz53cPcGLTRCy0BwCeMXJtI8Az6Xq2SNLOnfboilvLCgAAPEPwguBzoxeLk2UFAACeInhB8LnZi4WmdACQdwQvCL50XXedoCkdAOQdwQuCL9azRep5AJPpsgIAAM8RvCAcamvtaqFhw5zfl6Z0AOArBC8Ij9paafNm6aWX7NLoTA0fTpk0APgITeoQLr16SePH211zJ060b+va+t+yaEoHAD5G8IJwik0jJVougNb/AOBrBC8Ir2SLNzLKAgC+RvCCcOu6eCMAwPdI2AUAAEYheAEAAEYheAEAAEYheAEAAEYheAEAAEYheAEAAEYheAEAAEYheAEAAEYheAEAAEYJXIdd66+L7LW3t+d5TwAAQKZi523r0MVykwhc8LJ7925JUnl5eZ73BAAAOLV7924VFxen3CZiZRLiGKSjo0Pbt29Xv379FIlEXH3s9vZ2lZeXa+vWrSoqKnL1sf0g6M9PCv5z5PmZL+jPkednPq+eo2VZ2r17t8rKylRQkDqrJXAjLwUFBRo+fLinv6OoqCiwf5RS8J+fFPznyPMzX9CfI8/PfF48x3QjLjEk7AIAAKMQvAAAAKMQvDhQWFiouXPnqrCwMN+74omgPz8p+M+R52e+oD9Hnp/5/PAcA5ewCwAAgo2RFwAAYBSCFwAAYBSCFwAAYBSCFwAAYBSCl0P87Gc/09ixY9W3b1/1798/4TZbtmzReeedp759+2rIkCH68Y9/rIMHD6Z83J07d2rKlCkqKipS//79dfnll2vPnj0ePANnGhoaFIlEEl7eeOONpPc7++yzu21/1VVX5XDPM1dRUdFtX2+77baU9/niiy80ffp0DRw4UEceeaQuuOACtba25miPndm8ebMuv/xyjRw5UkcccYRGjRqluXPnav/+/Snv5+f38L777lNFRYX69OmjyspKvf766ym3f+qpp3T88cerT58+Oumkk/T888/naE+dW7Bggb75zW+qX79+GjJkiM4//3xt3Lgx5X2WLFnS7b3q06dPjvbYmVtuuaXbvh5//PEp72PS+yclPqZEIhFNnz494fZ+f/9effVVff/731dZWZkikYieeeaZTj+3LEtz5szR0KFDdcQRR6i6ulrvv/9+2sd1+jl2iuDlEPv379eFF16oq6++OuHPo9GozjvvPO3fv1+rVq3SI488oiVLlmjOnDkpH3fKlClat26dli9frt///vd69dVXdeWVV3rxFBwZO3asduzY0elyxRVXaOTIkTr99NNT3nfatGmd7nf77bfnaK+dmz9/fqd9vfbaa1Nuf/311+s///M/9dRTT+mVV17R9u3bVVtbm6O9dWbDhg3q6OjQ/fffr3Xr1mnhwoVavHixfvKTn6S9rx/fwyeffFIzZ87U3Llz9dZbb+mUU07RhAkT9NFHHyXcftWqVZo0aZIuv/xyvf322zr//PN1/vnn67333svxnmfmlVde0fTp0/XnP/9Zy5cv14EDB/Sd73xHe/fuTXm/oqKiTu/Vhx9+mKM9du7rX/96p3197bXXkm5r2vsnSW+88Uan57d8+XJJ0oUXXpj0Pn5+//bu3atTTjlF9913X8Kf33777br77ru1ePFirV69Wl/5ylc0YcIEffHFF0kf0+nnuEcsdPPwww9bxcXF3W5//vnnrYKCAqulpSV+23/8x39YRUVF1r59+xI+1l/+8hdLkvXGG2/Eb/vDH/5gRSIRq7m52fV9z8b+/futwYMHW/Pnz0+53VlnnWVdd911udmpLI0YMcJauHBhxtvv2rXLOvzww62nnnoqftv69estSVZjY6MHe+i+22+/3Ro5cmTKbfz6Hp5xxhnW9OnT4/+PRqNWWVmZtWDBgoTb/+AHP7DOO++8TrdVVlZaP/rRjzzdT7d89NFHliTrlVdeSbpNsuORH82dO9c65ZRTMt7e9PfPsizruuuus0aNGmV1dHQk/LlJ758k6+mnn47/v6OjwyotLbV+8YtfxG/btWuXVVhYaC1dujTp4zj9HPcEIy8ONDY26qSTTlJJSUn8tgkTJqi9vV3r1q1Lep/+/ft3Gsmorq5WQUGBVq9e7fk+O/G73/1On376qaZOnZp228cff1yDBg3SiSeeqNmzZ+uzzz7LwR72zG233aaBAwdqzJgx+sUvfpFymm/NmjU6cOCAqqur47cdf/zxOvroo9XY2JiL3c1aW1ubBgwYkHY7v72H+/fv15o1azq99gUFBaqurk762jc2NnbaXrI/kya9V5LSvl979uzRiBEjVF5erpqamqTHGz94//33VVZWpmOOOUZTpkzRli1bkm5r+vu3f/9+PfbYY/rhD3+YciFgk96/QzU1NamlpaXTe1RcXKzKysqk71FPPsc9EbiFGb3U0tLSKXCRFP9/S0tL0vsMGTKk022HHXaYBgwYkPQ++fLggw9qwoQJaRe2nDx5skaMGKGysjK98847uvHGG7Vx40bV19fnaE8z9y//8i/6xje+oQEDBmjVqlWaPXu2duzYobvuuivh9i0tLerdu3e3nKeSkhLfvV+JbNq0Sffcc4/uuOOOlNv58T385JNPFI1GE37GNmzYkPA+yT6TJrxXHR0dmjFjhv72b/9WJ554YtLtRo8erYceekgnn3yy2tradMcdd2js2LFat26d54vQOlVZWaklS5Zo9OjR2rFjh+bNm6dvf/vbeu+999SvX79u25v8/knSM888o127dumyyy5Luo1J719XsffByXvUk89xTwQ+eLnpppv085//POU269evT5tUZpKePOdt27bpxRdf1LJly9I+/qH5OieddJKGDh2q8ePH64MPPtCoUaN6vuMZcvL8Zs6cGb/t5JNPVu/evfWjH/1ICxYs8HX77p68h83NzTrnnHN04YUXatq0aSnvm+/3ENL06dP13nvvpcwJkaSqqipVVVXF/z927FidcMIJuv/++/XTn/7U69105Nxzz43/++STT1ZlZaVGjBihZcuW6fLLL8/jnnnjwQcf1LnnnquysrKk25j0/pkk8MHLrFmzUkbFknTMMcdk9FilpaXdMqZjVSilpaVJ79M1SengwYPauXNn0vtkqyfP+eGHH9bAgQP193//945/X2VlpST7W38uTnzZvKeVlZU6ePCgNm/erNGjR3f7eWlpqfbv369du3Z1Gn1pbW317P1KxOlz3L59u8aNG6exY8fqV7/6lePfl+v3MJFBgwapV69e3Sq7Ur32paWljrb3i2uuuSaevO/02/fhhx+uMWPGaNOmTR7tnXv69++vr371q0n31dT3T5I+/PBDvfTSS45HK016/2LvQ2trq4YOHRq/vbW1VaeeemrC+/Tkc9wjrmXPBEi6hN3W1tb4bffff79VVFRkffHFFwkfK5aw++abb8Zve/HFF32VsNvR0WGNHDnSmjVrVo/u/9prr1mSrP/+7/92ec/c99hjj1kFBQXWzp07E/48lrD7m9/8Jn7bhg0bfJ2wu23bNuu4446zLr74YuvgwYM9egy/vIdnnHGGdc0118T/H41GrWHDhqVM2P3e977X6baqqirfJnx2dHRY06dPt8rKyqz/+Z//6dFjHDx40Bo9erR1/fXXu7x37tu9e7d11FFHWb/85S8T/ty09+9Qc+fOtUpLS60DBw44up+f3z8lSdi944474re1tbVllLDr5HPco3117ZEC4MMPP7Tefvtta968edaRRx5pvf3229bbb79t7d6927Is+4/uxBNPtL7zne9Ya9eutV544QVr8ODB1uzZs+OPsXr1amv06NHWtm3b4redc8451pgxY6zVq1dbr732mnXcccdZkyZNyvnzS+all16yJFnr16/v9rNt27ZZo0ePtlavXm1ZlmVt2rTJmj9/vvXmm29aTU1N1rPPPmsdc8wx1plnnpnr3U5r1apV1sKFC621a9daH3zwgfXYY49ZgwcPti655JL4Nl2fn2VZ1lVXXWUdffTR1ssvv2y9+eabVlVVlVVVVZWPp5DWtm3brGOPPdYaP368tW3bNmvHjh3xy6HbmPIePvHEE1ZhYaG1ZMkS6y9/+Yt15ZVXWv37949X+P3TP/2TddNNN8W3/9Of/mQddthh1h133GGtX7/emjt3rnX44Ydb7777br6eQkpXX321VVxcbDU0NHR6rz777LP4Nl2f47x586wXX3zR+uCDD6w1a9ZYF198sdWnTx9r3bp1+XgKKc2aNctqaGiwmpqarD/96U9WdXW1NWjQIOujjz6yLMv89y8mGo1aRx99tHXjjTd2+5lp79/u3bvj5zpJ1l133WW9/fbb1ocffmhZlmXddtttVv/+/a1nn33Weuedd6yamhpr5MiR1ueffx5/jL/7u7+z7rnnnvj/032O3UDwcohLL73UktTtsnLlyvg2mzdvts4991zriCOOsAYNGmTNmjWrU+S9cuVKS5LV1NQUv+3TTz+1Jk2aZB155JFWUVGRNXXq1HhA5AeTJk2yxo4dm/BnTU1NnV6DLVu2WGeeeaY1YMAAq7Cw0Dr22GOtH//4x1ZbW1sO9zgza9assSorK63i4mKrT58+1gknnGD9+7//e6dRsq7Pz7Is6/PPP7f++Z//2TrqqKOsvn37Wv/wD//QKRjwk4cffjjh3+yhg6qmvYf33HOPdfTRR1u9e/e2zjjjDOvPf/5z/GdnnXWWdemll3baftmyZdZXv/pVq3fv3tbXv/5167nnnsvxHmcu2Xv18MMPx7fp+hxnzJgRfz1KSkqs7373u9Zbb72V+53PwEUXXWQNHTrU6t27tzVs2DDroosusjZt2hT/uenvX8yLL75oSbI2btzY7WemvX+xc1bXS+w5dHR0WP/2b/9mlZSUWIWFhdb48eO7Pe8RI0ZYc+fO7XRbqs+xGyKWZVnuTUIBAAB4iz4vAADAKAQvAADAKAQvAADAKAQvAADAKAQvAADAKAQvAADAKAQvAADAKAQvAADAKAQvAADAKAQvAADAKAQvAADAKAQvAADAKP8PRLYSdE6UiO0AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = sm.OLS(y_sin, X)  # Capital X, which has constants already\n",
    "results = model.fit()\n",
    "y_pred = results.predict(X)\n",
    "\n",
    "e_sin = y_pred - y_sin\n",
    "plt.plot(x, e_sin, 'ro')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is a pattern here (we will come to that, but the residuals are still centred around zero. Due to this, the most common cause of your residuals not being centred around zero is actually a *coding* error, where some issue in the handling of your data has occurred or a computer bug.\n",
    "\n",
    "That said, if you forget to add a constant, it can happen too. Here we fit a linear model to our linear data, but forget the constant:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x236a9541e90>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = sm.OLS(y_linear, x)  # lowercase x, with no constant\n",
    "results = model.fit()\n",
    "y_pred = results.predict(x)\n",
    "\n",
    "e_linear_no_constant = y_pred - y_linear\n",
    "plt.plot(x, e_linear_no_constant, 'ro')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here you can see the same spread of errors as our previous model, just not centred around zero. If you see errors not centred around zero, check for a constant, and then check your code for bugs! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise\n",
    "\n",
    "Write a function `fit_linear_plot_residuals` that takes the x and y values as input, fits a linear model, computes the residuals and then plots the residual plot. We will use this for the rest of our notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm\n",
    "def fit_linear_plot_residuals(x,y):\n",
    "    X = sm.add_constant(x)\n",
    "    model = sm.OLS(y, X)\n",
    "    results = model.fit()\n",
    "    y_pred = results.predict(X)\n",
    "    e_linear = y_pred - y\n",
    "    plt.title(\"Residual analysis - Linear\")\n",
    "    plt.plot(x, e_linear, 'ro')\n",
    "    plt.hlines(0, xmin=x.min(), xmax=x.max())   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*For solutions, see `solutions/fit_linear_plot_residuals.py`*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The next cell runs the solution, as it is needed. If you implemented your own (or improved it!)\n",
    "# then you can run your version here instead."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run -i solutions/fit_linear_plot_residuals.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit_linear_plot_residuals(x, y_linear)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Errors must look random\n",
    "\n",
    "In addition to being centred around zero, errors must \"look random\". We have formal methods for this, but when doing statistical analysis, a good starting point is to plot the residuals and just eyeball the results. We saw in the linear examples above, the residuals are scatted around 0, with no clear patterns. Let's look at a counter example: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# y = 3x**2 - 4x + 10 + e\n",
    "y_quad = 3 * x ** 2 - 4 * x + 10 + np.random.random(len(x)) * 90"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x236a998f910>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y_quad, 'bo')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit_linear_plot_residuals(x, y_quad)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we can see a clear pattern in the residuals - there is an area of negative residuals, then an area of positive residuals and then another area of negative residuals. Whenever you can predict a residual based on the previous residual, you have a pattern. More formally, we want residuals to be iid - that is, independently and identically distributed.\n",
    "\n",
    "Note that other patterns may exist too - for instance, if the errors consistently \"flip\" between positive and negative, that is another pattern that should be accounted for.\n",
    "\n",
    "For example, the BDS test statistic tests for independence in a time series. It tests the following hypotheses:\n",
    "\n",
    "* $H_0$: The data is independent and identically distributed\n",
    "* $H_A$: The data has some autocorrelation\n",
    "\n",
    "#### Exercise\n",
    "\n",
    "1. Using the `statsmodels.tsa.stattools.bds` function, test if the residuals above exhibit some autocorrelation.\n",
    "2. Using a different test from a previous notebook, test again for autocorrelation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Other patterns may be present in your data. For instance, seasonal trends are seen in many datasets, and this shows significantly in a residual plot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*For solutions, see `solutions/residual_analysis_one.py`*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# y = sin(2{pi}x/12) + 3x + e\n",
    "# x is \"months\" since start\n",
    "x = np.linspace(0, 36)\n",
    "y_seasonal = np.sin(x * 2 * np.pi / 12) + (0.5 * x) + np.random.random(len(x)) * 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x236a995a250>]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y_seasonal)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is a bit hard to see the seasonal trend, as it is masked by the strong linear trend and errors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit_linear_plot_residuals(x, y_seasonal)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even though the seasonal trend was present in the original data, it is more pronounced in the residual plot, which has the effect of demeaning, detrending and rescaling the data, showing patterns like this more clearly.\n",
    "\n",
    "#### Exercise\n",
    "\n",
    "Investigate the `statsmodels.tsa.seasonal.seasonal_decompose` method for removing a known seasonal trend from data. Remove the \"seasonal\" trend from the data above (assume that the x value is \"number of months\") and fit a linear model to the non-seasonal data. Check the residuals of this fit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The variability of the errors does not change\n",
    "\n",
    "A common issue that arises in datasets is that the variability of the errors changes with time (or increasing x for non-time series). This is a common occurrence in time series analysis. For example, as a stock price increases, a \"5% swing\" becomes a greater value. This is one reason to transform the data, but this pattern occurs in many other datasets. \n",
    "\n",
    "Let's have a look at some data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(-10, 10, 100)\n",
    "\n",
    "# y = 3x + 5 + e*x\n",
    "y_variation = 3 * x + 5 + np.random.random(len(x)) * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x23c427bca48>]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y_variation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit_linear_plot_residuals(x, y_variation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It may be tempting in the first plot (`x` versus `y_variation`) to simply discard the \"random noise\" at the top and bottom, but the residual plot highlights quite clearly that the variation changes dramatically as x does. The data starts with a very high variability, moves to a very low variability and then again to a very high variability. \n",
    "\n",
    "Important: \"high\" and \"low\" are subjective, and relative to the general variability in the data. Do not apply a blanket rule like \"variability above 4 is bad\".\n",
    "\n",
    "This data is said to have violated the assumption of homoscedasticity for OLS. In cases of strong variability, the OLS estimator is still consistent, and generally works \"well enough\". It would be important to report that estimations in the areas of high variability would have less precision than predictions in areas of low variability. Weighted least squares could help as well.\n",
    "\n",
    "If you have control over the data itself, investigate what is causing the variability and look to remove it. For instance, if we are measuring a car's performance, the variability might be high in the morning with a cold-start of the engine. As it warms up, the engine performs more consistently. Remove this impact, or fit the data to the different \"cold start\" and \"warm start\" categories."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise\n",
    "\n",
    "Create a plot with variability increasing over time, and plot the residual graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#from solutions\n",
    "y_increasing = np.random.random(len(x)) * np.arange(len(x)) * 25  # Your equation may vary\n",
    "\n",
    "plt.plot(x, y_increasing, 'bo')\n",
    "\n",
    "fit_linear_plot_residuals(x, y_increasing)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*For solutions, see `solutions/increasing_variability.py`*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### QQ plots\n",
    "\n",
    "A common method of analysing residuals is to look at the QQ plot, the quantile-quantile plot. It plots the quantiles of the residuals against the quantiles of a normal distribution. If the residuals are normally distributed, this plot will show a straight diagonal line with random variability around that line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.graphics.gofplots import qqplot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "qqplot(e_linear, line='s');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Question\n",
    "\n",
    "The errors are from a linear model fitting linear data with noise. Why isn't the plot above showing a straight line, and instead showing a clear pattern?\n",
    "\n",
    "Hint: Show a histogram of the errors and review the documentation of the qqplot graph."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Came from a uniform distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*For solutions, see `solutions/why_not_normal.py`*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we plot the QQ plot comparing the residuals to the x values, we get a straighter line and more randomness of the errors around this line. This would lead you to think that the errors are randomly distributed around that line:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.graphics.gofplots import qqplot_2samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "qqplot_2samples(x, e_linear, line='r');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In other words, this graph shows us that the errors do not seem to be dependent on the x variables.\n",
    "\n",
    "#### Exercise\n",
    "\n",
    "Plot the QQ plots (both against a normal distribution and a 2 sampled QQ plot) for the other datasets we generated in this module. What do their patterns show?\n",
    "\n",
    "#### Extended Exercise\n",
    "\n",
    "When fitting a linear model, a common visualisation is to output the following four graphs in a subplot with two columns and two rows:\n",
    "\n",
    "1. A plot comparing the Predicted values on (x-axis) against the Actual values (y-axis) with a diagonal line\n",
    "1. The residuals (y-axis) versus the x values scatter plot with a horizontal line at y=0\n",
    "1. A QQ plot of the residuals against a normal distribution\n",
    "1. A QQ plot of the residuals against the x values\n",
    "\n",
    "Create a function that takes the necessary inputs and produces these four plots. This function, or variations of it, are incredibly useful for future analysis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*For solutions see `solutions/residual_analysis_two.py`*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Autocorrelation in Residuals\n",
    "\n",
    "Another issue that can arise is when there is autocorrelation in the residuals. This happens when the data is noisy in the \"macro\" sense, but correlated in the \"micro\" sense.\n",
    "\n",
    "Here is an example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate a dataset\n",
    "# Errors have a autocorrelation with lag 1\n",
    "errors = np.random.randn(len(x)) * 3 + 5\n",
    "# Errors are dependent on the previous error to some degree\n",
    "errors[1:] += 0.5 * errors[:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "# y = mx + c + e\n",
    "y_corr = 2 * x + 6 + errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x23c42a7b288>]"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y_corr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit_linear_plot_residuals(x, y_corr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the above graph, the errors *look* random enough, and it would be hard to actually see any correlation here. Especially with so many data.\n",
    "\n",
    "However, let us extract the residuals and test for autocorrelation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.LineCollection at 0x23c42b16348>"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = sm.add_constant(x)\n",
    "model = sm.OLS(y_corr, X)  # Capital X, which has constants already\n",
    "results = model.fit()\n",
    "y_pred = results.predict(X)\n",
    "\n",
    "e_corr = y_pred - y_corr\n",
    "plt.plot(x, e_corr, 'ro')\n",
    "plt.hlines(0, xmin=x.min(), xmax=x.max())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.graphics.tsaplots import plot_acf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Object `autocorrelation_plot` not found.\n"
     ]
    }
   ],
   "source": [
    "autocorrelation_plot??"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_acf(e_corr, lags=20);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This plot shows a clear autocorrelation in the residuals at lag 1. Other values, such as 11 and 14 show a \"significant\" autocorrelation, but unless you had a significant reason to suspect a cyclic trend of this length (for instance, if your customers are on a 14 week rolling schedule), I would consider this \"unlucky\" in the null-hypothesis-false-positive sense.\n",
    "\n",
    "In this case, the residuals are not white noise and therefore we must examine for other trends in the data we are not accounting for. In this case, revisit some of the models we have seen, such as ARIMA, which is likely to be able to address this problem. In cases of autocorrelation, OLS is unable to adequately address the issue by itself."
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